Doppler sensors can be used to measure the relative speed between the sensor and a distant surface. This measurement is performed by projecting energy of a known frequency on the distant surface and comparing the returned energy frequency to the known frequency and inferring a speed based on the difference. To estimate the speed, a Doppler frequency shift is measured by estimating the frequency of the Doppler sensor output using a fast Fourier transform (FFT) or other estimation techniques, all of which require data collected over a fixed period of time.
A preferred output from a Doppler sensor is a speed measurement that is representative of a single instant in time, but this is physically impossible because frequency estimation requires a data sample collected in a time interval with non-zero length. Nevertheless, in near-constant relative speed environments, accurate measurements are possible. This is because constant relative speeds lead to continuous-time Doppler data with spectral density functions that are line spectra, and this is a fundamental assumption in most frequency estimation techniques. In dynamic environments, however, any relative speed change within the sample window will cause ambiguity in the frequency measurement due to the continuum of speeds present, which will cause the spectral density functions of the continuous-time Doppler data to take on a region of finite bandwidth. As a result, the spectral density function estimates of discretized Doppler data may have additional undesired effects due to leakage power or smearing bandwidth, which is dependent upon the discrete-data windowing function, the sample rate, and the underlying continuous-time spectral density function.
Typical Doppler implementations use a set of fixed algorithm parameters, designed to optimize measurement accuracy for a specific set of conditions, such as the case of continuous-time line spectra. When the frequency estimation techniques of the Doppler measurement algorithms are used outside of their designed conditions, measurement errors can occur.